Given Numbers are 273, 278

We can find the LCM of 273, 278 using the brute force method, prime factorization method, or GCD method.

To use brute force method, list the multiples of 273 and 278

Multiples of 273 =273,546,819,1092,1365,1638,1911,2184,2457,2730,3003,3276,3549,3822,4095,4368,4641,

Multiples of 278 =278,556,834,1112,1390,1668,1946,2224,2502,2780,3058,3336,3614,3892,4170,4448,4726,

Now, get the least common multiple of 273, 278 which is 75894

So, the LCM of 273, 278 is 75894.

One method for determining the LCM of 273 and 278 is to compare the prime factorization of each number. You can find the prime factorization for each number by following the instructions below:

Here is 273's prime factorization:

Prime factors of 273 are 3, 7,13.

273 = 3¹×7¹×13¹

And this is 278's prime factorization:

Prime factors of 278 are 2,139.

278 = 2¹×139¹

When comparing the prime factorization of these two numbers, look for the highest power to which each prime factor is raised. In this case, the following primary factors must be considered: 3, 7,13, 2,139

2¹×3¹×7¹×13¹×139¹ = 75894

This shows that the LCM of 273 and 278 is 75894.

The first step in determining the Least Common Multiple of 273 and 278 is to generate a list of multiples for each number.

Lets look at the multiples of these two numbers, 273 and 278:

Lets look at the first ten multiples of these numbers, 273 and 278:

273,546,819,1092,1365,1638,1911,2184,2457,4641 are the first ten multiples of 273.

278,556,834,1112,1390,1668,1946,2224,2502,4726 are the first ten multiples of 278.

You can continue to list the multiples of these numbers until you find a match. Once you have found a match, or several matches, the Least Common Multiple is the smallest of these matches. The first matching multiple(s) of 273 and 278, for example, are 3276, 4641, and 4448. 75894 is the least common multiple since it is the smallest.

273 and 278 have an LCM of 75894.

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 273 and 278, than apply into the LCM equation.

GCF(273,278) = 1
LCM(273,278) = ( 273 × 278) / 1
LCM(273,278) = 75894 / 1
LCM(273,278) = 75894

1. What is the LCM of 273 and 278?

The LCM of 273 and 278 is 75894.

2. How to find the lowest common multiple of 273 and 278?

To find the lowest common multiple of 273 and 278, we have to get the multip;es of both numbers and identify the least common multiple in them which is 75894.

3. What are the Factors of 273?

Answer: Factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273. There are 8 integers that are factors of 273. The greatest factor of 273 is 273.

4. What are the Factors of 278?

Answer: Factors of 278 are 1, 2, 139, 278. There are 4 integers that are factors of 278. The greatest factor of 278 is 278.

Answer:

Least Common Multiple of 273 and 278 = 75894

Step 1: Find the prime factorization of 273

273 = 3 x 7 x 13

Step 2: Find the prime factorization of 278

278 = 2 x 139

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 75894 = 2 x 3 x 7 x 13 x 139

Step 4: Therefore, the least common multiple of 273 and 278 is 75894.